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A Modified Discontinuous Galerkin Method for Solving Efficiently Helmholtz Problems

Published online by Cambridge University Press:  20 August 2015

Magdalena Grigoroscuta-Strugaru ,
Mohamed Amara ,
Henri Calandra  and
Rabia Djellouli
Magdalena Grigoroscuta-Strugaru*
Affiliation:
INRIA Bordeaux Sud-Ouest Research Center, Team Project Magique-3D and LMA/CNRS UMR 5142, Université de Pau et des Pays de l’Adour, France BCAM, Basque Center for Applied Mathematics, Bilbao, Spain
Mohamed Amara*
Affiliation:
INRIA Bordeaux Sud-Ouest Research Center, Team Project Magique-3D and LMA/CNRS UMR 5142, Université de Pau et des Pays de l’Adour, France
Henri Calandra*
Affiliation:
TOTAL, Avenue Larribau, Pau, France
Rabia Djellouli*
Affiliation:
Department of Mathematics, California State University Northridge and Interdisciplinary Research Institute for the Sciences, IRIS, USA
*
Email address:magdalena.grigoroscuta@univ-pau.fr
Email address:mohamed.amara@univ-pau.fr
Email address:henri.calandra@total.com
Corresponding author.Email:rabia.djellouli@csun.edu
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Abstract

A new solution methodology is proposed for solving efficiently Helmholtz problems. The proposed method falls in the category of the discontinuous Galerkin methods. However, unlike the existing solution methodologies, this method requires solving (a) well-posed local problems to determine the primal variable, and (b) a global positive semi-definite Hermitian system to evaluate the Lagrange multiplier needed to restore the continuity across the element edges. Illustrative numerical results obtained for two-dimensional interior Helmholtz problems are presented to assess the accuracy and the stability of the proposed solution methodology.

Keywords

35J0565N3049M2735L0593E24Helmholtz equationdiscontinuous Galerkinplane wavesLagrange multipliersinf-sup conditionwaveguide problems
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 335 - 350
Copyright
Copyright © Global Science Press Limited 2012

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References

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